The article "Detection and monitoring of the stick-slip motion: field experiments" by M. P. Dufeyte and H. Henneuse (SPE/IADC 21,945--Drilling Conference, Amsterdam, 11-14 March 1991) analyzes the stick-slip behaviour from measurements carded out by a device placed at the upper end of the drill string. If a stick-slip type dysfunction appears, this document recommends either to increase the rotary speed of the drill string from the rotary table, or to decrease the weight on the bit by acting on the drawworks.
The article "A study of slip-stick motion of the bit" by Kyllingstad A. and Halsey G. W. (SPE 16,659, 62nd Annual Technical Conference and Exhibition, Dallas, Sep. 27-30, 1987) analyzes the behaviour of a drill bit by using a pendular model.
The article "The Genesis of Bit-Induced Torsional Drillstring Vibrations" by J. F. Brett (SPE/IADC 21,943--Drilling Conference, Amsterdam, 11-14 March 1991) also describes the torsional vibrations induced by a PDC type bit.